1) Under invoking hubris, it says losers suffer wounds. But under battle it says the winner gets advantage die. I suspect the latter is correct. Am I right?

2) If I don't want to owe Achilles an Oath, can I turn down his offer of help? If so, can I hold off using his die and incuring an oath until I see how the initial rolls fall out?

3) How does Flee work? Does the player declare it in Break 1, then have to beat Position rolls in Exchange 2, fight Exchange 2, then flee?3a) Does the player still get to reposition a counter?3b) Can the player change his mind and stay?

1) I think you may be confusing two different things here, but then again I may be misunderstanding your question:

-> If you invoke Hubris, you as a player are refusing to accept the outcome of a simple contest, and turning it into a full battle. The stakes of the simple contest do not yet resolve, the loser(s) of the contest roll take a wound, and the you proceed to battle (i.e. an extended contest).

-> If the stakes of the simple contest was to gain an advantage die for use in a later conflict then the winner of that simple contest would get the advantage die. But if it was the players who lost, they could invoke Hubris (taking a wound) and turn the conflict over who gets the advantage die into a full battle itself.

2) The rule as John intended it does not allow you to turn down an offer of help. You can force an oath out of somebody this way. I'm not sure I'm a fan :)

3) Nobody has actually ever fled during battle in any game I played, but let me take a stab at this... I think you have the routine right in the main question. For 3a, I would say yes, and for 3b I would also say yes. I'm curious to see what John says :)